“Hello, Dolly is a piece of shit.”

This is the voice of Louis Armstrong, after the final concert of his life, as depicted in Terry Teachout’s first play, “Satchmo at the Waldorf,” a dramatic imagining of the private Pops, starring the extraordinary actor John Douglas Thompson. It is four months before his death in 1971, and Armstrong — who overcame poverty, outcast status and racism to become one of the most popular entertainers in the world — reaches first for the oxygen canister on the couch of his dressing room, taking a deep breath. Then he reaches for his tape recorder.

Teachout, the drama critic for the Wall Street Journal, authored “Pops: A Life of Louis Armstrong,” a 2009 biography of the famed trumpet player and singer known for his sunny disposition. The author discovered another side to the entertainer after listening to some of the hundreds of reels of tape that Armstrong recorded, a verbal diary that he kept over many years. It is those tapes that inform Teachout’s play.

The absorbing portrait that emerges over the 90-minute solo show at the Westside Theatre might be bracing for those who know Armstrong only as his public persona – and its epithet-happy dialogue might provide a bit of a jolt as well for the smaller subset of theatergoers who know Teachout only as a well-spoken critic and essayist. (At one point in the play, Armstrong, recalling his reaction to President Eisenhower’s initial refusal to intervene in the Little Rock integration crisis involving Arkansas Governor Orval Faubus, says: “Eisenhower, he don’t got no guts, he’s two- faced, won’t stand up to that no-good motherfucker Faubus.”)

For all its effort at showing something unfamiliar, “Satchmo at the Waldorf” doesn’t completely transcend the limitations of its formulaic genre. Like other solo shows of a celebrated figure who suddenly starts telling us the story of his life, it can feel too pat and too forced.

While there is a consensus that Armstrong was a musical genius, he was also apparently too modest and down-to-earth to accept or explain his own genius. (One can imagine a solo show about, say, Leonard Bernstein, having no such obstacle.) Teachout, who in an earlier career was himself a jazz musician, provides vivid details of Satchmo’s musicality in his biography, but the focus is elsewhere in the play.

There are two other characters in “Satchmo at the Waldorf” – Armstrong’s manager Joe Glaser, a tough-talker who used to work for Al Capone, and fellow jazz musician Miles Davis, who admired Armstrong’s trumpet-playing but considered him an Uncle Tom, an embarrassment to a new generation of African-Americans. If too much time is spent on Armstrong’s manager for my taste, their relationship ends in a startling revelation that could be considered the play’s climax.

Any quibbles about the script, however, largely disappear in light of the performance by John Douglas Thompson, who portrays all three characters in lightning-quick transitions that show off the actor’s own virtuosity. Thompson doesn’t attempt impersonations; what he offers is deeper and more persuasive. The play is given a first-rate production by director Gordon Edelstein, lighting designer Kevin Adams, and set designer Lee Savage, who works subtle wonders with the changes outside the dressing room window.

“Satchmo at the Waldorf” offers us a memorable mashup of the man we thought we knew with the one who apparently existed off-camera and off-stage. When in the play, Louis Armstrong’s rendition of “Hello, Dolly” knocks the Beatles off the top of the charts at the height of their popularity, making the sexagenarian the oldest musician to have a number one hit, his reaction sums up both sides of his character: “It’s still a piece of shit. But we gotta give the folks what they want.”

Satchmo at the Waldorf
Westside Theatre Upstairs
407 W 43rd St
Written by Terry Teachout
Directed by Gordon Edelstein
Set designed by Lee Savage, costumes designed by Ilona Somogyi, lighting designed by Kevin Adams
Cast: John Douglas Thompson
Running time: 90 minutes, no intermission
Tickets: $39 – $79